Question: Let $ x, y, z $ be positive real numbers such that $ x + y + z = 3 $. Find the minimum value of
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- Thus, the number of such functions is equal to the number of real constants $ k $, which is uncountably infinite. But if we are to count **distinct functions**, and assuming only linear solutions are acceptable, the number is infinite.
- However, if the problem is interpreted as asking for the number of **continuous** solutions, then the only such functions are linear: $ f(x) = kx $, and there are infinitely many such functions (one for each real $ k $).
- Hence, the number of such functions is $ \boxed{\infty} $, assuming no further restrictions.
- \frac{x^2}{y + z} + \frac{y^2}{z + x} + \frac{z^2}{x + y}.
- Solution: We are to minimize
- under the constraint $ x + y + z = 3 $.
